Baby Mental Life: Study 1

“Baby Mental Life: Study 1” was conducted on MTurk on 2018-07-31 through 2018-08-01.

Our planned sample was 300 participants, and we anticipated that roughly 85-90% of recruited participants would pass all of our attention checks, so we initially recruited 342 participants (on the idea that ~87.5% of 342 ~ 300 participants; note that for administrative purposes we need to recuit participants in batches that were divisible by 9). After filtering out participants who failed at least one of our attention checks, we ended up retaining only 80% of participants, so we recruited an additional 36 participants for a total of 378 people recruited (on the idea that ~80% of 378 ~ 300 participants; note that for administrative purposes we need to recuit participants in batches that were divisible by 9). In a slight deviation from our preregistered recruitment plan, we limited these additional 36 participants to women, because we had an unexpectedly large imbalance of men to women.

UPDATE: On 2018-08-09, KW discovered that there were many repeating GPS locations, a symptom of a recent outbreak of bots on MTurk. As of this date, these data have excluded any participants where there is another participant with an identical set of GPS coordinates as recorded by Qualtrics. This excluded an additional 76 participants (25%).

In the end, we ended up with a sample of 301 participants who passed our attention checks, 225 of whom came from unique GPS coordinates.

Each participant assessed children’s mental capacities at 3 target ages: newborns, 9-month-olds, and 5-year-olds. For each target, they rated 60 mental capacities on a scale from 0 (not at all capable) to 100 (completely capable).

For more details about the study, see our preregistration here.

# load required libraries
library(tidyverse)

── Attaching packages ──────────────────────────────────────── tidyverse 1.2.1 ──
✔ ggplot2 3.0.0     ✔ purrr   0.2.5
✔ tibble  1.4.2     ✔ dplyr   0.7.6
✔ tidyr   0.8.1     ✔ stringr 1.3.1
✔ readr   1.1.1     ✔ forcats 0.3.0
── Conflicts ─────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

library(langcog) # source: https://github.com/langcog/langcog-package

Attaching package: ‘langcog’

The following object is masked from ‘package:base’:

    scale

library(psych)

Attaching package: ‘psych’

The following objects are masked from ‘package:ggplot2’:

    %+%, alpha

library(lme4)

Loading required package: Matrix

Attaching package: ‘Matrix’

The following object is masked from ‘package:tidyr’:

    expand

# set theme for ggplots
theme_set(theme_bw())

# run source code (extra home-made functions)
source("./scripts/max_factors_efa.R")
source("./scripts/plot_fun.R")
source("./scripts/reten_fun.R")

Data preparation

# load in de-identified raw data
d0 <- read.csv("./data/deidentified/baby_mental_life_s1_data.csv") %>% select(-X)

# make question key
question_key <- d0[1,] %>%
  t() %>%
  data.frame() %>%
  rownames_to_column("question_qualtrics") %>%
  rename("question_text" = X1) %>%
  mutate(question = recode(question_qualtrics,
                           "Duration..in.seconds." = "Duration",
                           "Q2" = "Age",
                           "Q3" = "GenderSex",
                           "Q3_3_TEXT" = "GenderSex_fillIn",
                           "Q4" = "EnglishProf",
                           "Q5" = "FirstLang",
                           "Q5_2_TEXT" = "FirstLang_fillIn",
                           "Q18" = "RaceEthnicity",
                           "Q18_10_TEXT" = "RaceEthnicity_fillIn",
                           "Q19" = "Education",
                           "Q20" = "Income",
                           "Q21" = "MaritalStatus",
                           "Q21_6_TEXT" = "MaritalStatus_fillIn",
                           "Q22" = "HouseholdSize",
                           "Q23" = "Parent",
                           "Q25" = "ChildrenNumber",
                           "Q26" = "ChildrenYoungestAge",
                           "Q26_1_TEXT" = "ChildrenYoungestAge_fillIn1",
                           "Q26_2_TEXT" = "ChildrenYoungestAge_fillIn2",
                           "Q27" = "ChildrenOldestAge",
                           "Q27_1_TEXT" = "ChildrenOldestAge_fillIn1",
                           "Q27_2_TEXT" = "ChildrenOldestAge_fillIn2",
                           "Q28" = "Attention",
                           "Q29" = "Comments",
                           .default = question_qualtrics),
         question = case_when(grepl("the following questions", question_text) ~
                                gsub("^.*extent is a ", "", question_text),
                              TRUE ~ question),
         question = case_when(grepl("capable of...", question_text) ~
                                gsub("capable of... ", "", tolower(question)),
                              TRUE ~ question),
         question = gsub(" ", "_", question),
         question = gsub("'", "", question),
         question = gsub("newborn_-_", "target00mo_", question),
         question = gsub("9-month-old_-_", "target09mo_", question),
         question = gsub("5-year-old_-_", "target60mo_", question)) %>%
  mutate(question = gsub("-", "_", question),
         question = gsub(" \\(for_example,_smooth,_rough\\)", "", question))

# rename questions
d1 <- d0 %>%
  # get rid of extra info in first two rows  
  filter(!is.na(as.numeric(as.character(Q2)))) %>% 
  gather(question_qualtrics, response, -c(ResponseId, duplicateGPS)) %>%
  left_join(question_key %>% select(question_qualtrics, question)) %>%
  select(-question_qualtrics) %>%
  spread(question, response)

NAs introduced by coercionattributes are not identical across measure variables;
they will be droppedJoining, by = "question_qualtrics"

# implement inclusion/exclusion criteria
d2 <- d1 %>%
  filter(Age >= 18, Age <= 45,
         EnglishProf %in% c("Advanced", "Superior"),
         `target00mo_please_select_34` == 34,
         `target09mo_please_select_90` == 90,
         `target60mo_please_select_4` == 4,
         Attention == "Yes")

# remove people with another identical set of GPS coordinates among people who passed attention checks
d3 <- d2 %>%
  filter(duplicateGPS == F) %>%
  select(-duplicateGPS)

# recode variables & drop extraneous variables
d4 <- d3 %>%
  select(-c(EndDate, Finished, 
            payment, Progress, 
            RecordedDate, StartDate, Status, 
            timeEstimate, UserLanguage)) %>%
  mutate_at(vars(c(starts_with("target"), Age, ChildrenNumber, 
                   ChildrenOldestAge_fillIn1, ChildrenOldestAge_fillIn2, 
                   ChildrenYoungestAge_fillIn1, ChildrenYoungestAge_fillIn2,
                   Duration, HouseholdSize)),
            funs(as.numeric(.))) %>%
  mutate(Education = factor(Education,
                            levels = c("No schooling completed", 
                                       "Nursery school to 8th grade", 
                                       "Some high school, no diploma", 
                                       "High school graduate, diploma or equivalent (including GED)", 
                                       "Some college credit, no degree", 
                                       "Trade school, technical school, or vocational school",
                                       "Associate's degree (for example, AA, AS)",
                                       "Bachelor's degree (for example, BA, BS)",
                                       "Master's degree (for example, MA, MS)",
                                       "Doctor or professional degree (for example, PhD, JD, MD, MBA)")),
         Income = factor(Income,
                         levels = c("$5,001 - 15,000", 
                                    "$15,001 - 30,000", 
                                    "$30,001 - 60,000",
                                    "$60,001 - 90,000",
                                    "$90,001 - 150,000",
                                    "Greater than $150,000",
                                    "Prefer not to say")),
         Parent = factor(Parent,
                         levels = c("No", "Yes")))

NAs introduced by coercion

# make useful datasets
# final dataset with all measured variables
d <- d4 %>% distinct()
# demographic information
d_demo <- d %>% 
  select(ResponseId, Duration,
         Age, starts_with("GenderSex"), starts_with("RaceEthnicity"),
         starts_with("FirstLang"),
         Education, Income, HouseholdSize,
         starts_with("MaritalStatus"),
         Parent, starts_with("Children"), 
         Comments) %>%
  mutate(RaceEthnicity_collapse = ifelse(grepl(",([A-Za-z])", RaceEthnicity),
                                         "Multiple", RaceEthnicity)) %>%
  mutate(ChildrenOldestAge_collapse = case_when(
    ChildrenOldestAge %in% c("My oldest child has not yet been born (I am/my partner is pregnant)", "My oldest child is deceased", "Prefer not to say") ~ ChildrenOldestAge,
    ChildrenOldestAge == "In months:" ~ 
      ifelse(as.numeric(ChildrenOldestAge_fillIn1)/12 < 1,
             "< 1 year",
             ifelse(as.numeric(ChildrenOldestAge_fillIn1)/12 < 3, 
                    "1 - 3 years",
                    ifelse(as.numeric(ChildrenOldestAge_fillIn1)/12 < 5, 
                           "3 - 5 years",
                           ifelse(as.numeric(ChildrenOldestAge_fillIn1)/12 < 10, 
                                  "5 - 10 years",
                                  ifelse(as.numeric(ChildrenOldestAge_fillIn1)/12 < 18, 
                                         "10 - 18 years",
                                         "> 18 years"))))),
    ChildrenOldestAge == "In years:" ~
      ifelse(as.numeric(ChildrenOldestAge_fillIn2) < 1,
             "< 1 year",
             ifelse(as.numeric(ChildrenOldestAge_fillIn2) < 3, 
                    "1 - 3 years",
                    ifelse(as.numeric(ChildrenOldestAge_fillIn2) < 5, 
                           "3 - 5 years",
                           ifelse(as.numeric(ChildrenOldestAge_fillIn2) < 10, 
                                  "5 - 10 years",
                                  ifelse(as.numeric(ChildrenOldestAge_fillIn2) < 18, 
                                         "10 - 18 years",
                                         "> 18 years"))))),
    TRUE ~ "NA")) %>%
  mutate(ChildrenOldestAge_collapse = 
           factor(ChildrenOldestAge_collapse,
                  levels = c("My oldest child has not yet been born (I am/my partner is pregnant)",
                             "< 1 year",
                             "1 - 3 years",
                             "3 - 5 years",
                             "5 - 10 years",
                             "10 - 18 years",
                             "> 18 years",
                             "My oldest child is deceased",
                             "Prefer not to say"))) %>%
  mutate(ChildrenYoungestAge_collapse = case_when(
    ChildrenYoungestAge %in% c("My youngest child has not yet been born (I am/my partner is pregnant)", "My youngest child is deceased", "Prefer not to say") ~ ChildrenYoungestAge,
    ChildrenYoungestAge == "In months:" ~ 
      ifelse(as.numeric(ChildrenYoungestAge_fillIn1)/12 < 1,
             "< 1 year",
             ifelse(as.numeric(ChildrenYoungestAge_fillIn1)/12 < 3, 
                    "1 - 3 years",
                    ifelse(as.numeric(ChildrenYoungestAge_fillIn1)/12 < 5, 
                           "3 - 5 years",
                           ifelse(as.numeric(ChildrenYoungestAge_fillIn1)/12 < 10, 
                                  "5 - 10 years",
                                  ifelse(as.numeric(ChildrenYoungestAge_fillIn1)/12 < 18, 
                                         "10 - 18 years",
                                         "> 18 years"))))),
    ChildrenYoungestAge == "In years:" ~
      ifelse(as.numeric(ChildrenYoungestAge_fillIn2) < 1,
             "< 1 year",
             ifelse(as.numeric(ChildrenYoungestAge_fillIn2) < 3, 
                    "1 - 3 years",
                    ifelse(as.numeric(ChildrenYoungestAge_fillIn2) < 5, 
                           "3 - 5 years",
                           ifelse(as.numeric(ChildrenYoungestAge_fillIn2) < 10, 
                                  "5 - 10 years",
                                  ifelse(as.numeric(ChildrenYoungestAge_fillIn2) < 18, 
                                         "10 - 18 years",
                                         "> 18 years"))))),
    TRUE ~ "NA")) %>%
  mutate(ChildrenYoungestAge_collapse = 
           factor(ChildrenYoungestAge_collapse,
                  levels = c("My Youngest child has not yet been born (I am/my partner is pregnant)",
                             "< 1 year",
                             "1 - 3 years",
                             "3 - 5 years",
                             "5 - 10 years",
                             "10 - 18 years",
                             "> 18 years",
                             "My Youngest child is deceased",
                             "Prefer not to say")))  
# all assessments of ALL TARGETS, RepsonseId as rownames
d_all <- d %>% 
  select(ResponseId, starts_with("target"), -contains("please_select")) %>%
  gather(question, response, -ResponseId) %>%
  mutate(target = gsub("_.*$", "", question),
         capacity = gsub("target..mo_", "", question),
         subid = paste(ResponseId, target, sep = "_")) %>%
  select(-ResponseId, -question, -target) %>%
  spread(capacity, response) %>%
  column_to_rownames("subid")
# all assessments of NEWBORNS, RepsonseId as rownames
d_00mo <- d_all %>% 
  rownames_to_column("subid") %>%
  filter(grepl("target00mo", subid)) %>%
  mutate(subid = gsub("target..mo_", "", subid)) %>%
  column_to_rownames("subid")
# all assessments of 9-MONTH-OLDS, RepsonseId as rownames
d_09mo <- d_all %>% 
  rownames_to_column("subid") %>%
  filter(grepl("target09mo", subid)) %>%
  mutate(subid = gsub("target..mo_", "", subid)) %>%
  column_to_rownames("subid")
# all assessments of 5-YEAR-OLDS, RepsonseId as rownames
d_60mo <- d_all %>% 
  rownames_to_column("subid") %>%
  filter(grepl("target60mo", subid)) %>%
  mutate(subid = gsub("target..mo_", "", subid)) %>%
  column_to_rownames("subid")

EFA: all targets

Our primary analysis is an exploratory factor analysis (EFA) collapsing across all 3 target characters (and treating an individual participant’s responses to each character as if they were independent data points) - see the preregistration for more details.

We planned to examine three factor retention protocols in order to determine how many factors to retain: Parallel analysis, minimizing BIC, and a set of preset criteria outlined in Weisman et al. (2017). Here we look at each solution in turn.

Rotation choices

We planned to examine oblimin-rotated solutions (which allow factors to correlate), but you could examine other rotation options by selecting a different rotation type here.

chosen_rot <- "oblimin" # preregistered: factors allowed to correlate
# chosen_rot <- "varimax" # orthogonal: factors forced not to correlate
# chosen_rot <- "none" # no rotation

Parallel analysis

How many factors to retain?

reten_all_PA <- fa.parallel(d_all, plot = F); reten_all_PA

Parallel analysis suggests that the number of factors =  4  and the number of components =  3 
Call: fa.parallel(x = d_all, plot = F)
Parallel analysis suggests that the number of factors =  4  and the number of components =  3 

 Eigen Values of 

reten_all_par <- reten_all_PA$nfact

What are these factors?

efa_all_par <- fa(d_all, nfactors = reten_all_par, rotate = chosen_rot,
                  scores = "tenBerge", impute = "median")

 A loading greater than abs(1) was detected.  Examine the loadings carefully.

heatmap_fun(efa_all_par) + 
  labs(title = paste0("Parallel Analysis (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to which targets?

scoresplot_fun(efa_all_par, target = "all (study 1)") + 
  labs(title = "Parallel Analysis") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))

Ignoring unknown aesthetics: y

Here’s a multilevel linear regression on these factor scores, with random intercepts and slopes (for target and factor) by participant. Target is coded with linear and quadratic contrasts, and factor is effect-coded for comparison with the grand mean (with the last factor as the base, -1):

efa_all_par_scores <- efa_all_par$scores[] %>%
  data.frame() %>%
  rownames_to_column("subid") %>%
  mutate(target = gsub("^.*_target", "target", subid),
         ResponseId = gsub("_target.*$", "", subid)) %>%
  select(-subid) %>%
  gather(factor, score, -target, -ResponseId) %>%
  mutate_at(vars(target, factor), funs(factor))
contrasts(efa_all_par_scores$target) <- contr.poly(3)
contrasts(efa_all_par_scores$factor) <- contr.sum(reten_all_par)
r_all_par <- lmer(score ~ target * factor + (target + factor | ResponseId),
                  efa_all_par_scores)
summary(r_all_par, corr = F)

Linear mixed model fit by REML ['lmerMod']
Formula: score ~ target * factor + (target + factor | ResponseId)
   Data: efa_all_par_scores

REML criterion at convergence: 5181

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.2514 -0.5125  0.0304  0.5514  3.3609 

Random effects:
 Groups     Name        Variance Std.Dev. Corr                         
 ResponseId (Intercept) 0.26818  0.5179                                
            target.L    0.08540  0.2922   -0.44                        
            target.Q    0.02459  0.1568   -0.90  0.35                  
            factor1     0.11311  0.3363   -0.71  0.17  0.45            
            factor2     0.23800  0.4879    0.34  0.28  0.01 -0.71      
            factor3     0.02565  0.1602   -0.31 -0.22  0.43  0.53 -0.04
 Residual               0.23513  0.4849                                
Number of obs: 2700, groups:  ResponseId, 225

Fixed effects:
                   Estimate Std. Error t value
(Intercept)      -2.187e-15  3.576e-02   0.000
target.L          8.496e-01  2.531e-02  33.560
target.Q          7.120e-02  1.925e-02   3.699
factor1          -4.474e-16  2.764e-02   0.000
factor2           2.641e-15  3.632e-02   0.000
factor3           7.033e-17  1.937e-02   0.000
target.L:factor1  5.125e-01  2.800e-02  18.308
target.Q:factor1  2.749e-01  2.800e-02   9.819
target.L:factor2 -4.397e-01  2.800e-02 -15.707
target.Q:factor2 -1.117e-01  2.800e-02  -3.990
target.L:factor3  3.288e-01  2.800e-02  11.745
target.Q:factor3 -2.922e-01  2.800e-02 -10.439

If we consider t-values > 2 to be “significant” and use the plot above to guide our interpretation, here’s what we conclude:

• [(Intercept): By definition, because we’re using factor scores, which are similar to z-scores, the intercept is ~0.]
• target.L: Overall, mental capacity attributions increase with target age.
• target.Q: This increase is generally non-linear.
• [factor1, factor2, …: By definition, because we’re using factor scores, which are similar to z-scores, the differences in means across factors are ~0.]
• target.L:factor1: The linear increase is more dramatic (steeper slope) for MR1, compared to other factors.
• target.Q:factor1: The nonlinearity is more dramatic (curvier and/or concave instead of convex curve) for MR1, compared to other factors.
• target.L:factor2: The linear increase is less dramatic (shallower slope) for MR2, compared to other factors.
• target.Q:factor2: The nonlinearity is less dramatic (flatter curve) for MR2, compared to other factors.
• target.L:factor3: The linear increase is more dramatic (steeper slope) for MR3, compared to other factors.
• target.Q:factor3: The nonlinearity is less dramatic (flatter curve) for MR3, compared to other factors.

itemsplot_fun(efa_all_par, target = "all") + 
  labs(title = "Parallel Analysis")

Joining, by = "capacity"

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Joining, by = c("capacity", "factor", "order")

Minimizing BIC

How many factors to retain?

reten_all_vss <- VSS(d_all, plot = F); reten_all_vss

Very Simple Structure
Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
    n.obs = n.obs, plot = plot, title = title, use = use, cor = cor)
VSS complexity 1 achieves a maximimum of 0.96  with  1  factors
VSS complexity 2 achieves a maximimum of 0.99  with  2  factors

The Velicer MAP achieves a minimum of 0.01  with  6  factors 
BIC achieves a minimum of  -6032.72  with  6  factors
Sample Size adjusted BIC achieves a minimum of  -1597.88  with  8  factors

Statistics by number of factors 
  vss1 vss2    map  dof chisq     prob sqresid  fit RMSEA   BIC SABIC
1 0.96 0.00 0.0520 1710 15608  0.0e+00    53.5 0.96 0.112  4468  9898
2 0.60 0.99 0.0134 1651  7366  0.0e+00    11.9 0.99 0.073 -3390  1853
3 0.44 0.88 0.0076 1593  5252  0.0e+00     8.4 0.99 0.060 -5126   -68
4 0.42 0.80 0.0058 1536  4124 2.4e-235     6.5 0.99 0.051 -5883 -1006
5 0.41 0.79 0.0057 1480  3667 4.4e-186     5.9 1.00 0.048 -5974 -1275
6 0.42 0.80 0.0056 1425  3251 6.4e-144     5.5 1.00 0.045 -6033 -1508
7 0.42 0.80 0.0059 1371  3016 3.6e-125     5.2 1.00 0.044 -5915 -1562
8 0.42 0.80 0.0062 1318  2804 3.5e-109     4.9 1.00 0.042 -5783 -1598
  complex eChisq  SRMR eCRMS  eBIC
1     1.0  27560 0.107 0.109 16420
2     1.5   3161 0.036 0.038 -7595
3     1.9   1548 0.025 0.027 -8830
4     2.2    803 0.018 0.020 -9203
5     2.3    623 0.016 0.018 -9018
6     2.4    511 0.015 0.016 -8772
7     2.4    448 0.014 0.016 -8483
8     2.4    390 0.013 0.015 -8196

reten_all_bic <- data.frame(reten_all_vss$vss.stats %>%
  rownames_to_column("nfactors") %>%
  top_n(-1, BIC) %>%
  select(nfactors))$nfactors %>% as.numeric()

What are these factors?

efa_all_bic <- fa(d_all, nfactors = reten_all_bic, rotate = chosen_rot,
                  scores = "tenBerge", impute = "median")

convergence not obtained in GPFoblq. 1000 iterations used. A loading greater than abs(1) was detected.  Examine the loadings carefully.

heatmap_fun(efa_all_bic) + 
  labs(title = paste0("Minimizing BIC (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to which targets?

scoresplot_fun(efa_all_bic, target = "all (study 1)") + 
  labs(title = "Minimizing BIC") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))

Ignoring unknown aesthetics: y

Here’s a multilevel linear regression on these factor scores, with random intercepts and slopes (for target and factor) by participant. Target is coded with linear and quadratic contrasts, and factor is effect-coded for comparison with the grand mean (with the last factor as the base, -1):

efa_all_bic_scores <- efa_all_bic$scores[] %>%
  data.frame() %>%
  rownames_to_column("subid") %>%
  mutate(target = gsub("^.*_target", "target", subid),
         ResponseId = gsub("_target.*$", "", subid)) %>%
  select(-subid) %>%
  gather(factor, score, -target, -ResponseId) %>%
  mutate_at(vars(target, factor), funs(factor))
contrasts(efa_all_bic_scores$target) <- contr.poly(3)
contrasts(efa_all_bic_scores$factor) <- contr.sum(reten_all_bic)
r_all_bic <- lmer(score ~ target * factor + (target + factor | ResponseId),
                  efa_all_bic_scores,
                  control = lmerControl(optCtrl = list(maxfun = 100000)))

If we consider t-values > 2 to be “significant” and use the plot above to guide our interpretation, here’s what we conclude:

• [(Intercept): By definition, because we’re using factor scores, which are similar to z-scores, the intercept is ~0.]
• target.L: Overall, mental capacity attributions increase with target age.
• target.Q: This increase is not generally non-linear.
• [factor1, factor2, …: By definition, because we’re using factor scores, which are similar to z-scores, the differences in means across factors are ~0.]
• target.L:factor1: The linear increase is more dramatic (steeper slope) for MR1, compared to other factors.
• target.Q:factor1: The nonlinearity is more dramatic (curvier and/or concave instead of convex curve) for MR1, compared to other factors.
• target.L:factor2: The linear increase is less dramatic (shallower slope) for MR2, compared to other factors.
• target.Q:factor2: The nonlinearity for MR2 is comparable to other factors.
• target.L:factor3: The linear increase is more dramatic (steeper slope) for MR3, compared to other factors.
• target.Q:factor3: The nonlinearity is less dramatic (flatter curve) for MR3, compared to other factors.
• target.L:factor4: The linear increase is less dramatic (shallower slope) for MR4, compared to other factors.
• target.Q:factor4: The nonlinearity is more dramatic (curvier and/or concanve instead of convex curve) for MR4, compared to other factors.
• target.L:factor5: The linear increase is more dramatic (steeper slope) for MR5, compared to other factors.
• target.Q:factor5: The nonlinearity is less dramatic (flatter curve) for MR5, compared to other factors.

itemsplot_fun(efa_all_bic, target = "all") + 
  labs(title = "Minimizing BIC")

Joining, by = "capacity"

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Joining, by = c("capacity", "factor", "order")

Preset retention criteria

How many factors to retain?

reten_all_k <- reten_fun(d_all, rot_type = chosen_rot)
print(paste("Preset criteria suggest retaining", reten_all_k, "factors"))

[1] "Preset criteria suggest retaining 2 factors"

What are these factors?

efa_all_k <- fa(d_all, nfactors = reten_all_k, rotate = chosen_rot,
                  scores = "tenBerge", impute = "median")

heatmap_fun(efa_all_k) + 
  labs(title = paste0("Preset criteria (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to which targets?

scoresplot_fun(efa_all_k, target = "all (study 1)") + 
  labs(title = "Preset factor retention criteria (Weisman et al., 2017)")

Ignoring unknown aesthetics: y

Here’s a multilevel linear regression on these factor scores, with random intercepts and slopes (for target and factor) by participant. Target is coded with linear and quadratic contrasts, and factor is effect-coded for comparison with the grand mean (with the last factor as the base, -1):

efa_all_k_scores <- efa_all_k$scores[] %>%
  data.frame() %>%
  rownames_to_column("subid") %>%
  mutate(target = gsub("^.*_target", "target", subid),
         ResponseId = gsub("_target.*$", "", subid)) %>%
  select(-subid) %>%
  gather(factor, score, -target, -ResponseId) %>%
  mutate_at(vars(target, factor), funs(factor))
contrasts(efa_all_k_scores$target) <- contr.poly(3)
contrasts(efa_all_k_scores$factor) <- contr.sum(reten_all_k)
r_all_k <- lmer(score ~ target * factor + (target + factor | ResponseId),
                efa_all_k_scores)
summary(r_all_k, corr = F)

Linear mixed model fit by REML ['lmerMod']
Formula: score ~ target * factor + (target + factor | ResponseId)
   Data: efa_all_k_scores

REML criterion at convergence: 2466.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.7025 -0.4841  0.0034  0.5413  2.7814 

Random effects:
 Groups     Name        Variance Std.Dev. Corr             
 ResponseId (Intercept) 0.26690  0.5166                    
            target.L    0.08731  0.2955   -0.48            
            target.Q    0.02408  0.1552   -0.93  0.26      
            factor1     0.09109  0.3018   -0.63 -0.09  0.48
 Residual               0.18763  0.4332                    
Number of obs: 1350, groups:  ResponseId, 225

Fixed effects:
                   Estimate Std. Error t value
(Intercept)       3.800e-15  3.640e-02   0.000
target.L          1.050e+00  2.837e-02  36.991
target.Q          3.457e-02  2.289e-02   1.510
factor1          -1.095e-15  2.332e-02   0.000
target.L:factor1  3.327e-01  2.042e-02  16.292
target.Q:factor1  2.042e-01  2.042e-02   9.999

There are some problems with this model that I haven’t addressed - see warnings above. Ignoring them for now…

If we consider t-values > 2 to be “significant” and use the plot above to guide our interpretation, here’s what we conclude:

• [(Intercept): By definition, because we’re using factor scores, which are similar to z-scores, the intercept is ~0.]
• target.L: Overall, mental capacity attributions increase with target age.
• target.Q: This increase is generally non-linear.
• [factor1: By definition, because we’re using factor scores, which are similar to z-scores, the differences in means across factors are ~0.]
• target.L:factor1: The linear increase is more dramatic (steeper slope) for MR1, compared to other factors.
• target.Q:factor1: The nonlinearity is more dramatic (curvier and/or concave instead of convex curve) for MR1, compared to other factors.

itemsplot_fun(efa_all_k, target = "all") + 
  labs(title = "Preset factor retention criteria (Weisman et al., 2017)")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

EFA: newborns

What happens if we limit ourselves to assessments of newborns’ mental capacities?

Parallel analysis

How many factors to retain?

reten_00mo_PA <- fa.parallel(d_00mo, plot = F); reten_00mo_PA

Parallel analysis suggests that the number of factors =  4  and the number of components =  3 
Call: fa.parallel(x = d_00mo, plot = F)
Parallel analysis suggests that the number of factors =  4  and the number of components =  3 

 Eigen Values of 
  Original factors Simulated data Original components simulated data
1            20.21           1.26               20.83           2.20
2             6.83           1.09                7.59           2.07
3             1.76           1.01                2.47           1.99
4             1.25           0.94                1.87           1.93

reten_00mo_par <- reten_00mo_PA$nfact

What are these factors?

efa_00mo_par <- fa(d_00mo, nfactors = reten_00mo_par, rotate = chosen_rot,
                  scores = "tenBerge", impute = "median")

heatmap_fun(efa_00mo_par) + 
  labs(title = paste0("Parallel Analysis (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to newborns?

itemsplot_fun(efa_00mo_par, target = "newborns") + 
  labs(title = "Parallel Analysis")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

Minimizing BIC

How many factors to retain?

reten_00mo_vss <- VSS(d_00mo, plot = F); reten_00mo_vss

Very Simple Structure
Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
    n.obs = n.obs, plot = plot, title = title, use = use, cor = cor)
VSS complexity 1 achieves a maximimum of 0.83  with  1  factors
VSS complexity 2 achieves a maximimum of 0.94  with  2  factors

The Velicer MAP achieves a minimum of 0.01  with  5  factors 
BIC achieves a minimum of  -5953.64  with  3  factors
Sample Size adjusted BIC achieves a minimum of  -1158.37  with  8  factors

Statistics by number of factors 
  vss1 vss2    map  dof chisq     prob sqresid  fit RMSEA   BIC SABIC
1 0.83 0.00 0.0329 1710  4978 1.1e-315      87 0.83 0.100 -4284  1135
2 0.67 0.94 0.0124 1651  3203 5.4e-102      29 0.94 0.072 -5739  -506
3 0.59 0.92 0.0094 1593  2674  5.4e-58      23 0.96 0.062 -5954  -905
4 0.44 0.78 0.0087 1536  2407  1.3e-41      20 0.96 0.058 -5912 -1044
5 0.43 0.79 0.0086 1480  2223  7.5e-33      18 0.96 0.055 -5793 -1103
6 0.43 0.78 0.0087 1425  2080  2.0e-27      17 0.97 0.054 -5638 -1122
7 0.43 0.77 0.0089 1371  1950  4.9e-23      16 0.97 0.052 -5475 -1130
8 0.43 0.76 0.0092 1318  1803  9.5e-18      15 0.97 0.050 -5335 -1158
  complex eChisq  SRMR eCRMS  eBIC
1     1.0  13387 0.130 0.132  4125
2     1.4   2498 0.056 0.058 -6444
3     1.6   1609 0.045 0.047 -7019
4     1.9   1207 0.039 0.042 -7112
5     2.0   1030 0.036 0.039 -6985
6     2.1    895 0.034 0.037 -6823
7     2.3    785 0.031 0.036 -6640
8     2.3    697 0.030 0.034 -6441

reten_00mo_bic <- data.frame(reten_00mo_vss$vss.stats %>%
  rownames_to_column("nfactors") %>%
  top_n(-1, BIC) %>%
  select(nfactors))$nfactors %>% as.numeric()

What are these factors?

efa_00mo_bic <- fa(d_00mo, nfactors = reten_00mo_bic, rotate = chosen_rot,
                   scores = "tenBerge", impute = "median")

heatmap_fun(efa_00mo_bic) + 
  labs(title = paste0("Minimizing BIC (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to newborns?

itemsplot_fun(efa_00mo_bic, target = "newborns") + 
  labs(title = "Minimizing BIC")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

Preset retention criteria

How many factors to retain?

reten_00mo_k <- reten_fun(d_00mo, rot_type = chosen_rot)
print(paste("Preset criteria suggest retaining", reten_00mo_k, "factors"))

[1] "Preset criteria suggest retaining 2 factors"

What are these factors?

efa_00mo_k <- fa(d_00mo, nfactors = reten_00mo_k, rotate = chosen_rot,
                 scores = "tenBerge", impute = "median")

heatmap_fun(efa_00mo_k) + 
  labs(title = paste0("Preset criteria (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to newborns?

itemsplot_fun(efa_00mo_k, target = "newborns") + 
  labs(title = "Preset factor retention criteria\n(Weisman et al., 2017)")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

EFA: 9-month-olds

What happens if we limit ourselves to assessments of 9-month-olds’ mental capacities?

Parallel analysis

How many factors to retain?

reten_09mo_PA <- fa.parallel(d_09mo, plot = F); reten_09mo_PA

Parallel analysis suggests that the number of factors =  4  and the number of components =  3 
Call: fa.parallel(x = d_09mo, plot = F)
Parallel analysis suggests that the number of factors =  4  and the number of components =  3 

 Eigen Values of 
  Original factors Simulated data Original components simulated data
1            26.33           1.24               26.86           2.18
2             7.41           1.09                8.07           2.07
3             1.46           1.01                2.04           1.99
4             1.14           0.93                1.67           1.91

reten_09mo_par <- reten_09mo_PA$nfact

What are these factors?

efa_09mo_par <- fa(d_09mo, nfactors = reten_09mo_par, rotate = chosen_rot,
                   scores = "tenBerge", impute = "median")

heatmap_fun(efa_09mo_par) + 
  labs(title = paste0("Parallel analysis (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to 9-month-olds?

itemsplot_fun(efa_09mo_par, target = "9-month-olds") + 
  labs(title = "Parallel Analysis")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

Minimizing BIC

How many factors to retain?

reten_09mo_vss <- VSS(d_09mo, plot = F); reten_09mo_vss

Very Simple Structure
Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
    n.obs = n.obs, plot = plot, title = title, use = use, cor = cor)
VSS complexity 1 achieves a maximimum of 0.9  with  1  factors
VSS complexity 2 achieves a maximimum of 0.98  with  2  factors

The Velicer MAP achieves a minimum of 0.01  with  5  factors 
BIC achieves a minimum of  -5884.26  with  4  factors
Sample Size adjusted BIC achieves a minimum of  -1149.05  with  8  factors

Statistics by number of factors 
  vss1 vss2    map  dof chisq     prob sqresid  fit RMSEA   BIC SABIC
1 0.90 0.00 0.0486 1710  5771  0.0e+00    84.4 0.90 0.110 -3490  1929
2 0.67 0.98 0.0138 1651  3394 9.8e-123    19.3 0.98 0.076 -5548  -316
3 0.47 0.87 0.0106 1593  2826  7.0e-72    15.2 0.98 0.066 -5802  -754
4 0.43 0.76 0.0090 1536  2435  7.3e-44    12.6 0.98 0.059 -5884 -1016
5 0.42 0.75 0.0088 1480  2241  3.7e-34    11.2 0.99 0.056 -5775 -1085
6 0.42 0.75 0.0088 1425  2082  1.5e-27    10.3 0.99 0.054 -5636 -1120
7 0.42 0.74 0.0089 1371  1939  2.5e-22     9.5 0.99 0.052 -5486 -1141
8 0.41 0.74 0.0092 1318  1812  2.6e-18     8.8 0.99 0.050 -5326 -1149
  complex eChisq  SRMR eCRMS  eBIC
1     1.0  14525 0.135 0.137  5264
2     1.4   1763 0.047 0.049 -7179
3     1.8   1147 0.038 0.040 -7481
4     2.1    785 0.031 0.034 -7534
5     2.2    642 0.028 0.031 -7374
6     2.3    546 0.026 0.029 -7172
7     2.4    474 0.024 0.028 -6951
8     2.4    417 0.023 0.027 -6721

reten_09mo_bic <- data.frame(reten_09mo_vss$vss.stats %>%
  rownames_to_column("nfactors") %>%
  top_n(-1, BIC) %>%
  select(nfactors))$nfactors %>% as.numeric()

What are these factors?

efa_09mo_bic <- fa(d_09mo, nfactors = reten_09mo_bic, rotate = chosen_rot,
                   scores = "tenBerge", impute = "median")

heatmap_fun(efa_09mo_bic) + 
  labs(title = paste0("Minimizing BIC (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to 9-month-olds?

itemsplot_fun(efa_09mo_bic, target = "9-month-olds") + 
  labs(title = "Minimizing BIC")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

Preset retention criteria

How many factors to retain?

reten_09mo_k <- reten_fun(d_09mo, rot_type = chosen_rot)
print(paste("Preset criteria suggest retaining", reten_09mo_k, "factors"))

[1] "Preset criteria suggest retaining 2 factors"

What are these factors?

efa_09mo_k <- fa(d_09mo, nfactors = reten_09mo_k, rotate = chosen_rot,
                 scores = "tenBerge", impute = "median")

heatmap_fun(efa_09mo_k) + 
  labs(title = paste0("Preset criteria (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to 9-month-olds?

itemsplot_fun(efa_09mo_k, target = "9-month-olds") + 
  labs(title = "Preset factor retention criteria\n(Weisman et al., 2017)")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

EFA: 5-year-olds

What happens if we limit ourselves to assessments of 5-year-olds’ mental capacities?

Parallel analysis

How many factors to retain?

reten_60mo_PA <- fa.parallel(d_60mo, plot = F); reten_60mo_PA

Parallel analysis suggests that the number of factors =  3  and the number of components =  2 
Call: fa.parallel(x = d_60mo, plot = F)
Parallel analysis suggests that the number of factors =  3  and the number of components =  2 

 Eigen Values of 
  Original factors Simulated data Original components simulated data
1            32.53           1.29               32.96           2.23
2             6.13           1.11                6.67           2.09
3             1.27           1.01                1.76           1.99

reten_60mo_par <- reten_60mo_PA$nfact

What are these factors?

efa_60mo_par <- fa(d_60mo, nfactors = reten_60mo_par, rotate = chosen_rot,
                   scores = "tenBerge", impute = "median")

 A loading greater than abs(1) was detected.  Examine the loadings carefully.

heatmap_fun(efa_60mo_par) + 
  labs(title = paste0("Parallel analysis (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to 5-year-olds?

itemsplot_fun(efa_60mo_par, target = "5-year-olds") + 
  labs(title = "Parallel Analysis")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

Minimizing BIC

How many factors to retain?

reten_60mo_vss <- VSS(d_60mo, plot = F); reten_60mo_vss

Very Simple Structure
Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
    n.obs = n.obs, plot = plot, title = title, use = use, cor = cor)
VSS complexity 1 achieves a maximimum of 0.95  with  1  factors
VSS complexity 2 achieves a maximimum of 0.99  with  2  factors

The Velicer MAP achieves a minimum of 0.01  with  5  factors 
BIC achieves a minimum of  -4460.84  with  4  factors
Sample Size adjusted BIC achieves a minimum of  61.81  with  8  factors

Statistics by number of factors 
  vss1 vss2   map  dof chisq     prob sqresid  fit RMSEA   BIC SABIC
1 0.95 0.00 0.053 1710  7316  0.0e+00    58.4 0.95 0.129 -1945  3474
2 0.62 0.99 0.016 1651  4777 1.1e-300    14.0 0.99 0.099 -4165  1067
3 0.49 0.84 0.013 1593  4219 4.5e-236    10.9 0.99 0.093 -4409   639
4 0.52 0.79 0.013 1536  3858 8.0e-200     9.4 0.99 0.090 -4461   407
5 0.49 0.77 0.012 1480  3594 1.3e-176     8.2 0.99 0.088 -4422   269
6 0.46 0.78 0.013 1425  3391 2.8e-161     7.5 0.99 0.086 -4327   189
7 0.52 0.77 0.013 1371  3219 8.2e-150     6.8 0.99 0.086 -4207   138
8 0.50 0.76 0.013 1318  3023 2.5e-135     6.2 0.99 0.084 -4115    62
  complex eChisq  SRMR eCRMS  eBIC
1     1.0  10123 0.113 0.115   862
2     1.5   1386 0.042 0.043 -7556
3     1.9    938 0.034 0.036 -7690
4     2.1    728 0.030 0.032 -7591
5     2.2    597 0.027 0.030 -7419
6     2.2    522 0.026 0.029 -7196
7     2.2    455 0.024 0.027 -6971
8     2.3    394 0.022 0.026 -6744

reten_60mo_bic <- data.frame(reten_60mo_vss$vss.stats %>%
  rownames_to_column("nfactors") %>%
  top_n(-1, BIC) %>%
  select(nfactors))$nfactors %>% as.numeric()

What are these factors?

efa_60mo_bic <- fa(d_60mo, nfactors = reten_60mo_bic, rotate = chosen_rot,
                   scores = "tenBerge", impute = "median")

heatmap_fun(efa_60mo_bic) + 
  labs(title = paste0("Minimizing BIC (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to 5-year-olds?

itemsplot_fun(efa_60mo_bic, target = "5-year-olds") + 
  labs(title = "Minimizing BIC")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

Preset retention criteria

How many factors to retain?

reten_60mo_k <- reten_fun(d_60mo, rot_type = chosen_rot)
print(paste("Preset criteria suggest retaining", reten_60mo_k, "factors"))

[1] "Preset criteria suggest retaining 2 factors"

What are these factors?

efa_60mo_k <- fa(d_60mo, nfactors = reten_60mo_k, rotate = chosen_rot,
                 scores = "tenBerge", impute = "median")

heatmap_fun(efa_60mo_k) + 
  labs(title = paste0("Preset criteria (rotation: ", chosen_rot, ")"),
       subtitle = "'% var.' indicates the amount of shared variance explained (total = 100%)")

Joining, by = "capacity"
Joining, by = "factor"

Which capacities are attributed to 5-year-olds?

itemsplot_fun(efa_60mo_k, target = "5-year-olds") + 
  labs(title = "Preset factor retention criteria\n(Weisman et al., 2017)")

Joining, by = "capacity"
Joining, by = c("capacity", "factor", "order")

Demographics

ggplot(d_demo, aes(x = Duration/60)) + 
  geom_histogram(binwidth = 2) +
  geom_vline(xintercept = median(d_demo$Duration/60), color = "blue", lty = 2) +
  scale_x_continuous(breaks = seq(0, 10000, 4)) +
  labs(title = "Duration of study (according to Qualtrics)",
       subtitle = "Blue dotted line marks median",
       x = "Duration (in minutes)",
       y = "Number of participants")

ggplot(d_demo, aes(x = Age)) + 
  geom_histogram(binwidth = 2) +
  geom_vline(xintercept = median(d_demo$Age), color = "blue", lty = 2) +
  scale_x_continuous(breaks = seq(0, 10000, 4)) +
  labs(title = "Particpiant age (self-reported)",
       subtitle = "Blue dotted line marks median",
       x = "Age (in years)",
       y = "Number of participants")

ggplot(d_demo, aes(x = GenderSex)) + 
  geom_bar() +
  labs(title = "Particpiant gender/sex (self-reported)",
       x = "Gender/sex",
       y = "Number of participants")

ggplot(d_demo, aes(x = gsub('(.{1,30})(\\s|$)', '\\1\n', RaceEthnicity_collapse))) + 
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1)) +
  labs(title = "Particpiant race/ethnicity (self-reported)",
       x = "Race/ethnicity",
       y = "Number of participants")

ggplot(d_demo, aes(x = FirstLang)) + 
  geom_bar() +
  labs(title = "Particpiant first language (self-reported)",
       x = "Language",
       y = "Number of participants")

ggplot(d_demo, aes(x = factor(Education,
                              levels = levels(d$Education),
                              labels = gsub('(.{1,30})(\\s|$)', '\\1\n', 
                                            levels(d$Education))))) + 
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1)) +
  labs(title = "Particpiant educational attainment (self-reported)",
       x = "Highest level of education completed",
       y = "Number of participants")

ggplot(d_demo, aes(x = Income)) + 
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1)) +
  labs(title = "Particpiant household income (self-reported)",
       x = "Annual household income",
       y = "Number of participants")

ggplot(d_demo, aes(x = HouseholdSize)) + 
  geom_histogram(binwidth = 1) +
  geom_vline(xintercept = median(d_demo$HouseholdSize), color = "blue", lty = 2) +
  scale_x_continuous(breaks = seq(0, 10000, 1)) +
  labs(title = "Particpiant household size (self-reported)",
       subtitle = "Blue dotted line marks median",
       x = "Number of people in household (adults and children)",
       y = "Number of participants")

ggplot(d_demo, aes(x = MaritalStatus)) + 
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1)) +
  labs(title = "Particpiant marital status (self-reported)",
       x = "Marital status",
       y = "Number of participants")

ggplot(d_demo, aes(x = Parent)) + 
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1)) +
  labs(title = "Particpiant parent status (self-reported)",
       subtitle = "'NA' indicates response of 'Prefer not to say'",
       x = "Parent status",
       y = "Number of participants")

ggplot(d_demo %>% filter(Parent == "Yes"), aes(x = ChildrenNumber)) + 
  geom_histogram(binwidth = 1) +
  geom_vline(xintercept = median(d_demo[d_demo$Parent == "Yes",]$ChildrenNumber, na.rm = T), 
             color = "blue", lty = 2) +
  scale_x_continuous(breaks = seq(0, 10000, 1)) +
  labs(title = "Number of children among parents (self-reported)",
       subtitle = "Blue dotted line marks median",
       x = "Number of children (among parents)",
       y = "Number of participants")

ggplot(d_demo %>% filter(Parent == "Yes"), 
       aes(x = factor(ChildrenOldestAge_collapse,
                      levels = levels(d_demo$ChildrenOldestAge_collapse),
                      labels = gsub('(.{1,30})(\\s|$)', '\\1\n', 
                                    levels(d_demo$ChildrenOldestAge_collapse))))) + 
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1)) +
  labs(title = "Age of oldest child among parents (self-reported)",
       x = "Age of child in years (among parents)",
       y = "Number of participants")

ggplot(d_demo %>% filter(Parent == "Yes"), 
       aes(x = factor(ChildrenYoungestAge_collapse,
                      levels = levels(d_demo$ChildrenYoungestAge_collapse),
                      labels = gsub('(.{1,30})(\\s|$)', '\\1\n', 
                                    levels(d_demo$ChildrenYoungestAge_collapse))))) + 
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1)) +
  labs(title = "Age of youngest child among parents (self-reported)",
       x = "Age of child in years (among parents)",
       y = "Number of participants")

Save EFA output

Finally, I’ll export the 4-factor EFA results to a saved file that I can draw on in our Study 2 analyses.

saveRDS(efa_all_par, file = "./s1_efa.rds")

Error in saveRDS(efa_all_par, file = "./s1_efa.rds") : 
  object 'efa_all_par' not found